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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-06 13:54:02 UTC</tt>.<br>
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| : The original revision id was <tt>362584284</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | The [[patent val]] of 185edo [[tempering out|tempers out]] [[126/125]], [[1029/1024]], [[6144/6125]] in the 7-limit, and [[243/242]] in the 11-limit, making it useful for various purposes. It is an excellent tuning for [[starling]], the [[7-limit]] [[planar temperament]] tempering out 126/125; [[valentine]], which also tempers out 1029/1024; and [[cuckoo]], tempering out 126/125 and 243/242. |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
| | Using the 185c val, it tempers out [[225/224]] and 1029/1024 in the 7-limit, 243/242, [[385/384]], [[441/440]], and [[540/539]] in the 11-limit, providing a great alternative to [[72edo]] for [[miracle]]. With the 185cf val {{val| 185 293 '''429''' 519 640 '''684''' }}, it makes for an excellent tuning of 13-limit [[manna]]. Meanwhile the 185cff val {{val| 185 293 '''429''' 519 640 '''686''' }} is a first-class tuning of 13-limit [[miraculous]]. |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">**185edo** divides the [[octave]] into 185 equal steps of size 6.4865 [[cent]]s each. It [[tempering out|tempers out]] the [[comma]]s 126/125, 1029/1024, 6144/6125 and 243/242, making it useful for various purposes. It is an excellent tuning for [[Starling family|starling temperament]], the [[7-limit]] [[planar temperament]] tempering out 126/125; [[Starling family#Valentine temperament|valentine temperament]], which also tempers out 1029/1024; and the rank three 89&154&185 temperament tempering out 126/125 and 243/242. With 185dff, the val <185 293 429 519 640 686|, it makes for a first-class tuning of the 13-limit [[Gamelismic clan#Miracle-Miraculous|miraculous temperament]].
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| | === Odd harmonics === |
| | {{Harmonics in equal|185}} |
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| | === Subsets and supersets === |
| | Since 185 factors into {{factorization|185}}, 185edo contains [[5edo]] and [[37edo]] as its subsets. |
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| == Scales == | | == Scales == |
| * [[nova]] | | * [[nova]] |
| * [[novadene]]</pre></div> | | * [[novadene]] |
| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>185edo</title></head><body><strong>185edo</strong> divides the <a class="wiki_link" href="/octave">octave</a> into 185 equal steps of size 6.4865 <a class="wiki_link" href="/cent">cent</a>s each. It <a class="wiki_link" href="/tempering%20out">tempers out</a> the <a class="wiki_link" href="/comma">comma</a>s 126/125, 1029/1024, 6144/6125 and 243/242, making it useful for various purposes. It is an excellent tuning for <a class="wiki_link" href="/Starling%20family">starling temperament</a>, the <a class="wiki_link" href="/7-limit">7-limit</a> <a class="wiki_link" href="/planar%20temperament">planar temperament</a> tempering out 126/125; <a class="wiki_link" href="/Starling%20family#Valentine temperament">valentine temperament</a>, which also tempers out 1029/1024; and the rank three 89&amp;154&amp;185 temperament tempering out 126/125 and 243/242. With 185dff, the val &lt;185 293 429 519 640 686|, it makes for a first-class tuning of the 13-limit <a class="wiki_link" href="/Gamelismic%20clan#Miracle-Miraculous">miraculous temperament</a>.<br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Scales"></a><!-- ws:end:WikiTextHeadingRule:0 --> Scales </h2>
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| <ul><li><a class="wiki_link" href="/nova">nova</a></li><li><a class="wiki_link" href="/novadene">novadene</a></li></ul></body></html></pre></div>
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| Prime factorization
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5 × 37
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| Step size
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6.48649 ¢
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| Fifth
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108\185 (700.541 ¢)
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| Semitones (A1:m2)
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16:15 (103.8 ¢ : 97.3 ¢)
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| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
185 equal divisions of the octave (abbreviated 185edo or 185ed2), also called 185-tone equal temperament (185tet) or 185 equal temperament (185et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 185 equal parts of about 6.49 ¢ each. Each step represents a frequency ratio of 21/185, or the 185th root of 2.
Theory
The patent val of 185edo tempers out 126/125, 1029/1024, 6144/6125 in the 7-limit, and 243/242 in the 11-limit, making it useful for various purposes. It is an excellent tuning for starling, the 7-limit planar temperament tempering out 126/125; valentine, which also tempers out 1029/1024; and cuckoo, tempering out 126/125 and 243/242.
Using the 185c val, it tempers out 225/224 and 1029/1024 in the 7-limit, 243/242, 385/384, 441/440, and 540/539 in the 11-limit, providing a great alternative to 72edo for miracle. With the 185cf val ⟨185 293 429 519 640 684], it makes for an excellent tuning of 13-limit manna. Meanwhile the 185cff val ⟨185 293 429 519 640 686] is a first-class tuning of 13-limit miraculous.
Odd harmonics
Approximation of odd harmonics in 185edo
| Harmonic
|
3
|
5
|
7
|
9
|
11
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13
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15
|
17
|
19
|
21
|
23
|
| Error
|
Absolute (¢)
|
-1.41
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+2.88
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-2.34
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-2.83
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+0.03
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+2.72
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+1.46
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-1.17
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+0.87
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+2.73
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+0.91
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| Relative (%)
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-21.8
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+44.3
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-36.1
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-43.6
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+0.5
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+41.9
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+22.5
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-18.1
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+13.3
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+42.1
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+14.1
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Steps
(reduced)
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293
(108)
|
430
(60)
|
519
(149)
|
586
(31)
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640
(85)
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685
(130)
|
723
(168)
|
756
(16)
|
786
(46)
|
813
(73)
|
837
(97)
|
Subsets and supersets
Since 185 factors into 5 × 37, 185edo contains 5edo and 37edo as its subsets.
Scales